Improving the option pricing performance of GARCH models in inefficient market

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Understanding the relation between option pricing and market efficiency is important. Indeed, emphasizing this relation generates new insights that are appropriate in practice. These insights give a better understanding of the current limitations of the option pricing and hedging methods. This article thus aims to improve the performance of the option pricing approach. To start, the relation between the option pricing methodology and the informational market efficiency was discussed. It is, therefore, useful, before proceeding to apply the standard risk-neutral approach, to check the efficiency assumption. New modified GARCH processes were used to model the dynamics of the asset returns in the option pricing framework. The new considered approaches allow describing the dynamic of returns when the market is inefficient. Using real data on CAC 40 index, the performance of different models as a function of maturity and moneyness was studied. The in-sample analysis, interested in the stability of the pricing models across time, showed that the new approach, developed under the affine GARCH process, is the most accurate. The study of the out-of-sample performance, which aims to evaluate the forecasting ability of different approaches, confirmed the results of the in-sample analysis. For the optional portfolio hedging, always the best hedging approach is that obtained under the affine GARCH model. After a regression study, it was found that the difference between theoretical and observed option values can be explained by factors, which are not taken into account in the proposed pricing formulae.

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    • Figure 1. Autocorrelation functions of the CAC 40 index price, log-price and log-return (12/31/1987 – 12/31/2018)
    • Figure 2. Statistical t-test of the parameter θ
    • Figure 3. In-sample average absolute errors as a function of maturity
    • Figure 4. In-sample average absolute errors as a function of moneyness
    • Figure 5. Hedging absolute errors as a function of moneyness
    • Table 1. Estimations and properties (daily returns of CAC 40 from January 1988 to December 2012)
    • Table 2. Goodness-of-fit of the TFS-GARCH models
    • Table 3. Out-of-sample forecast errors as a function of the maturity
    • Table 4. Out-of-sample forecast errors as a function of moneyness